Higher November 2020 Paper 1 Q19
19 Without using a calculator, rationalise the denominator of \(\dfrac{6}{3 - \sqrt{7}}\)
Simplify your answer.
You must show each stage of your working.
(3)
| Scheme | Marks |
|---|---|
\(\dfrac{6}{3 - \sqrt{7}} \times \dfrac{3 + \sqrt{7}}{3 + \sqrt{7}}\) or \(\dfrac{6}{3 - \sqrt{7}} \times \dfrac{-3 - \sqrt{7}}{-3 - \sqrt{7}}\) | M1 |
\(\dfrac{6(3 + \sqrt{7})}{3^2 - 7}\) or \(\dfrac{6(3 + \sqrt{7})}{2}\) or \(\dfrac{6(-3 - \sqrt{7})}{-3^2 + 7}\) or \(\dfrac{6(-3 - \sqrt{7})}{-2}\) | M1 |
Working required Answer: \(9 + 3\sqrt{7}\) | A1 |
| (3) | |
| (3 marks) |
Notes
M1: (numerator may be expanded or denominator may be 4 terms which need to be all correct)
A1: dep on M2
for \(9 + 3\sqrt{7}\) or \(3(3 + \sqrt{7})\) from correct working